The average rate of change (AROC) of a function f(x) on an interval [a, b] is equal to the slope of the secant line to the graph of f(x) that passes through (a, f(a)) and (b, f(b)), a.k.a. the difference quotient given by
![f_{\mathrm{AROC}[a,b]} = \dfrac{f(b)-f(a)}{b-a}](https://tex.z-dn.net/?f=f_%7B%5Cmathrm%7BAROC%7D%5Ba%2Cb%5D%7D%20%3D%20%5Cdfrac%7Bf%28b%29-f%28a%29%7D%7Bb-a%7D)
So for f(x) = x² on [1, 5], the AROC of f is
![f_{\mathrm{AROC}[1,5]} = \dfrac{5^2-1^2}{5-1} = \dfrac{24}4 = \boxed{6}](https://tex.z-dn.net/?f=f_%7B%5Cmathrm%7BAROC%7D%5B1%2C5%5D%7D%20%3D%20%5Cdfrac%7B5%5E2-1%5E2%7D%7B5-1%7D%20%3D%20%5Cdfrac%7B24%7D4%20%3D%20%5Cboxed%7B6%7D)
45x+30= price for electrician when x= hours
To convert hour into minute: (No. of hour × 60) minutes
So, 2/5 hours = (2/5 × 60) minutes = (120/5) minutes = 24 minutes
Answer:
450 people paid the discounted fare and 750 people paid the regular fare.
Step-by-step explanation:
let r be regular fares paid and d be discounted fares paid
Total fares = 0.8r + 0.4d = 780
Since 1200 people paid the fares,
r + d = 1200 = Total people
Rearrange this formula:
r = 1200 - d
Substitute r into Total Fares formula
Total fares = 0.8r + 0.4d
780 = 0.8(1200-d) + 0.4d
780 = 960 - 0.8d + 0.4d
780 = 960 - 0.4d
0.4d = 180
d = 450
Sub d=450 into Total people formula
r + d = 1200 = Total people
r + 450 = 1200
r = 1200-450
r = 750
450 people paid the discounted fare and 750 people paid the regular fare.
A rate is a special ratio in which the two terms are in different units. A rate is a little bit different than the ratio, it is a special ratio. For this case, the rate would have units of miles per minutes. We calculate as follows:
rate = 36 miles / 45 min = 0.8 miles per min
distance traveled = 0.8 miles per min ( 60 min ) = 48 miles
